If the 2011's ECU had never been updated it could just be that the 2013 is running 240E. That and it has some thousands of miles less on the odometer.
My 2010 is now running 240E plus the BPM tune and it is almost like a different car. My car only has 4,744 miles too so it's almost new.
There is no reason to believe that BMW made any improvements other than in software. Their decontenting and changes in materials tell a different story, one of decreasing unit cost.
2015 BMW M5 Sedan M-DCT w/Competition Pkg and Carbon Ceramic Brakes, Driver's Assistance, and Executive Pkgs, B&O, Alpine White / Sakhir Orange and Black Full Leather, lots of carbon fiber, and a Trunk Monkey called "Der Stig".